Abstract: We argue that a microscopic structure for spacetime such as that expected in a quantum foam scenario, in which microscopic wormholes and other topological structures should play a relevant role, might lead to an effective metric-affine geometry at larger scales. This idea is supported by the role that microscopic defects play in crystalline structures. With an explicit model, we show that wormhole formation is possible in a metric-affine scenario, where the wormhole and the matter fields play a role analogous to that of defects in crystals. Such wormholes also arise in Born-Infeld gravity, which is favored by an analogy with the estimated mass of a point defect in condensed matter systems. We also point out that in metric-affine geometries, Einstein's equations with an effective cosmological constant appear as an attractor in the vacuum limit for a vast family of theories of gravity. This illustrates how lessons from solid state physics can be useful in unveiling the properties of the microcosmos and defining new avenues for modified theories of gravity.

Abstract: Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K (R beta μnu R alpha beta μnu)-R-alpha, can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the connection.

Abstract: The optical appearance of a body compact enough to feature an unstable bound orbit, when surrounded by an accretion disk, is expected to be dominated by a luminous ring of radiation enclosing a central brightness depression typically known as the shadow. Despite observational limitations, the rough details of this picture have been now confirmed by the results of the Event Horizon Telescope (EHT) Collaboration on the imaging of the M87 and Milky Way supermassive central objects. However, the precise characterization of both features-ring and shadow-depends on the interaction between the background geometry and the accretion disk, thus being a fertile playground to test our theories on the nature of compact objects and the gravitational field itself in the strong-field regime. In this work we use both features in order to test a continuous family of solutions interpolating between regular black holes and horizonless compact objects, which arise within the Eddington-inspired Born-Infeld theory of gravity, a viable extension of Einstein's general relativity (GR). To this end we consider seven distinctive classes of such configurations (five black holes and two traversable wormholes) and study their optical appearances under illumination by a geometrically and optically thin accretion disk, emitting monochromatically with three analytic intensity profiles previously suggested in the literature. We build such images and consider the sub-ring structure created by light rays crossing the disk more than once and existing on top of the main ring of radiation. We discuss in detail the modifications as compared to their GR counterparts, the Lyapunov exponents of unstable nearly-bound orbits, as well as the differences between black hole and traversable wormholes for the three intensity profiles. In addition we use the claim by the EHT Collaboration on the radius of the bright ring acting (under proper calibrations) as a proxy for the radius of the shadow itself to explore the parameter space of our solutions compatible with such a result.

Abstract: Inspired by the peculiarities of the effective geometry of crystalline structures, we reconsider thick brane scenarios from a metric-affine perspective. We show that for a rather general family of theories of gravity, whose Lagrangian is an arbitrary function of the metric and the Ricci tensor, the background and scalar field equations can be written in first-order form, and tensorial perturbations have a non negative definite spectrum, which makes them stable under linear perturbations regardless of the form of the gravity Lagrangian. We find, in particular, that the tensorial zero modes are exactly the same as predicted by Einstein's theory regardless of the scalar field and gravitational Lagrangians.

Abstract: Effective geometries arising from a hypothetical discrete structure of spacetime can play an important role in the understanding of the gravitational physics beyond General Relativity (GR). To discuss this question, we make use of lessons from crystalline systems within solid state physics, where the presence of defects in the discrete microstructure of the crystal determine the kind of effective geometry needed to properly describe the system in the macroscopic continuum limit. In this work, we study metric-affine theories with nonmetricity and torsion, which are the gravitational analog of crystalline structures with point defects and dislocations. We consider a crystal-motivated gravitational action and show the presence of topologically nontrivial structures (wormholes) supported by an electromagnetic field. Their existence has important implications for the quantum foam picture and the effective gravitational geometries. We discuss how the dialogue between solid state physics systems and modified gravitational theories can provide useful insights on both sides.